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I would say just a little bit about the notion of fractals. Generally because this word has been tossed about here much and it's important to understand it. fractals are self-similar curves, that means they're objects made of tiny versions of themselves. that's all it really means.
They can be quite simple mathematical objects such as a circle. The curve of a circle is curved in the same way no matter how large or small a portion of it you look at it has this fractal quality. but most fractals are very complex. a common example of a fractal in nature is a fern or a feather. you must have noticed how a fern is made up of little fern-like structures which are made up of still smaller fern-like structures coming off a vein and and some ferns have four or five levels of these little fern declining.
The fractal thing if you've not heard of it before you heard it here first and it's going to give very powerful mathematical tools to us for the description of reality you see. Until the fractals were legitimized by high-speed computers the only objects we had to describe nature were the classic aristotelian solids the cube, the perfect sphere, the ellipse, the rhomboid the parallel, that was it.
2500 years we've been trying to get along with that, and obviously these things do not describe nature very well. That was the whole problem that hung astronomy for a thousand to fifteen hundred years. They had perfect circles to describe the motion of the planets and the planets all moved in ellipses so then to get their perfect circles to work they had to invent the ptolemaic epicycle which was this excruciatingly inelegant way of causing an ellipse to appear to be a system of perfect circles.
Until fairly recently these kind of curves which were really discovered and described in the late 19th century were pretty much ignored. They were called pathological curves, the reason being that it was felt that their mathematics was so complicated that their end states couldn't be calculated and so they were called pathological. This all changed with the invention of computers, because they are not problems so complicated that computers can't solve them.
So suddenly the pathological curves which before had been very hard to visualize at all it became possible to create animated computer graphic movies of these things and what was amazing about them was some families of these curves had looked like river deltas, nerve branchings, tree lines, coast lines, island chains, there were was this astonishing tendency for some families of these curves to look like natural objects and at first nobody knew exactly what to do with this.
Fractals are described by mathematicians as occupying intermediate dimensions. Another name for them is space filling curves. If you ask what is the dimension of the fractal you will be given a number between one and two like 1.365 these things occupy an intermediate zone they are neither quite two-dimensional nor entirely one-dimensional, or not quite three-dimensional nor entirely two-dimensional and it's this inter-dimensionality of the fractal also that holds possibility. It occupies an intermediate dimension between whole numbers.
IBM now has programs that produce endless landscapes. These computer graphic movies of fractals, it shows you what looks like a mountain range running down to one side of the screen and the camera focuses in on this point in the side of the screen and mountain range flows out of it for as long as you care to look at it. Hours, days, weeks, it doesn't care. Just keep blowing up this point and you see more and more landscape.
You just fly above snow-capped mountain ranges with alpine lakes and then lower altitude areas with river cut uplands and then more mountains, and more lakes, and more deserts, and more rivers, and it just goes on and on. It's being created from a few lines of computer code in a raster scanning graphics system and immediately natural scientists grabbed onto these things to describe aspects of nature that had been previously outside the realm of calculation because you can perform a certain kind of almost magic with these things.
As an example of how it works once that ohio foundation we were on a at point saul which is a huge beach near vandenberg air force base and it runs for miles with the long low sand dunes coming in and i was walking on this beach and it was swept clean. i mean it was virtually there was nothing on it and i came upon a heavy black pebble and i noticed this heavy black pebble sitting there with a little pattern around it. it had obviously been deposited by the incoming tide and i kept walking along this beach and after about a while i came upon an identical black pebble just like the first one.
Finally, I had a stroke of insight, or the Logos tapped me on the shoulder, and i decided i would perform an experiment. At the second black pebble I turned and retraced my steps and i counted my steps until i had returned to the first black pebble. It was like 723 steps. So then i continued walking and 730 steps later there was an identical third black pebble sitting on the beach.
Well, if I had had some credulous person with me i'm sure I could have won big money by this method! But what is happening is not mysterious at all. It's that the sea rolling into this huge bay represents a very large unresolved set of equations for chaos and turbulence. It sorts itself out in such a way that there are hierarchical patterns of movement and force in the tide, such that every 725 steps give or take five steps the equation solves itself in such a way to deposit a black rock on the beach.
This verges on almost natural magic or something, and what it allows in the hands of cybernetic modelers is the possibility that very very complex natural systems such as the drainage of river basins, the energy economy of a rain forest, or something like that will be found to resolve itself into rather simple kinds of mathematically describable objects.
The thing to notice about fractals, the way they do their magic is that they are nested. The same set of perturbations, or the same set of value changes are nested again and again into each other on many many levels. So that what is implied if we say that there's a fractal description of the rain forest, and there's a fractal description of river systems, and there's a fractal description of the coastline, of the continents, what that implies is that there therefore must be a fractal in which all of those fractals are somehow subsets and that the planet itself is some kind of fractal object.
To my mind I mean that's all now agreed on by these guys like Mandelbrot and Pikekin and the people who are working with all of this, but to my mind the the next step in that is to extend the notion of fractalness to time. There is this funny perception that every day is somehow like every other, which is different from saying that every day is made of four other days, but every day is rather like every other, and every week is rather like every other week, and every year, and every century, and every million years is rather like the one that came before.
Generally that's the rule but what the fractal shows is how you can have this repetition and everything embedded in sameness and the momentum if you will of the morphogenetic field and still have occasionally completely astonishing events occur. That's the thing, how to save the phenomenon of extreme perturbation and still be true to this tendency that the universe has to smooth all perturbations.
If you want to see an example of a great mind anticipating a mathematical breakthrough you all know 'the wave' by hokusai writes the great japanese printmaker. well sometime next time you see it look at the place where the wave is coming over the top and beginning to break apart because what you'll you have this one wave coming up, and then it divides into two, and then they divide each into two, and each into two and there's this wonderful fractal drip on the lip of the wave that you know is the product of very keen observation.
Also leonardo da vinci believe it or not did a series of drawings of turbulence. Can you imagine drawing turbulence? He would drop he would drop ink in glasses of water and then draw it and he drew it with such an attention to detail that the fractal nature of turbulence of that sort is visible in the drawings. Of course there was no name for it or anything this guy just had such an eye.
What made them very exciting to me was when you give them to a good computer and it generates these things for you they look more like hallucinations than any art of the huichol or the wetoto, i mean these things look like hallucinations well so that's very suggestive because you think:
These mathematical objects look like hallucinations, so do hallucinations look like these mathematical objects because the nervous system is organized this way and we're somehow getting an organizational insight into how either the physical matter is arranged or how the data is being handled and this may be the key you know if language turns out to be fractal well. This is the key to understanding, learning, memory.
It sort of explains how we can be in the world because what it's saying is you know if you find out about this square yard of ground you're in a much better position to deal with all other square yards of ground, though not a perfect position. In other words that local information has global implications.
This notion of local information having global implications is a a cardinal principle of shamanism you see, the idea and it's exemplified in volume and private and all this talk about calligraphy and all this it's that locally is the information that you need to have to understand uh distant situations it is all there and it is it achieves this through a basic organizational principle the holographic,the hologrammatic, the fractal enfolding of information so that no matter how small a piece of the puzzle you have if you meditate deeply enough the entire pattern can be extracted out of it.
One of the great problems of computer artificial language theory is the problem of getting a machine to recognize all possible sentences as sentences. we seem to do this quite naturally, I mean every day if you live with exciting people you hear sentences which were probably never before spoken in the history of the world, and yet you immediately understand that this is a sentence. But getting a machine to achieve this kind of linguistic closure is very difficult. Now with the parallel processing machines and fractal analysis of language they think they're going to get it.
The language laboratory at MIT is doing a lot of work on it. A fair bit of it is classified because it revolves around the government funds what are called machine translation projects and that's doing the spade work for artificial language projects they want to have voice controlled fighter aircraft and stuff like this and you know they begin with very simple vocabularies but the idea is to build out and this kind of effort will not be successful unless we really know what language is because we're trying to get down on the nitty-gritty of it.The fractal thing it's very interesting i mean it has implications sociologically for our own psychological self-imaging, for planning and yet once grasped it's a very simple notion.
Now linguistic analysis is being carried out that shows that syntax is fractally organized that the act of creating language is the act of running a fractal generation program in the human neurological system and that somehow if you analyze speech hours and hours of speech. God knows i'm aware of the fractal nature of speech because i'm always in the same place saying the same thing but it's always a little different.
I don't quite understand the fractals in language. What is it that's being repeated, is it tones, or what is the syntactical patterns of subject, object, relationship modified by phrases in a certain way. the fact that adjectives perceive normally what they modify, yes exactly that there are these patterns.
The idea of fractals is reinforced by the natural world. Everywhere we look there are cycles. Energy cycles, astrophysical cycles, the spinning planet, but we we have for a long time seen these things as cycles but we've never seen them as repeated repetitive modules of large fractal systems which is what they really are. it isn't that the earth always goes around the sun the same way, it's that it more or less goes around the sun the same way and nested uh systems of fractals. You know the I-ching uses this wonderful phrase "pre-potent systems of relationship" and says you must not come into conflict with pre-potent systems of relationship. this means do not walk into closed doors. now if the door is closed please open it before passing through otherwise you get a bump on the head.
knowing that the universe has this fractal structure makes it possible to navigate through it, even if you don't buy into this particular version of fractal metaphors. Fractal ways of thinking about things are going to make life much easier to live in the future. i think it was janice joplin or some people say andy warhol and that proves the point before i even tell the anecdote anyway one or the other of them said "in the future everybody will be famous for 15 minutes" well this is a perfect exemplification of a fractal sociological point of view, i mean whichever said it they were quite a master.
And i think this is what wisdom must be in life, it's the ability to be handed a situation, you know your daughter's running off with the hell's angel, or your bank account is overdrawn, and knowing how to solve it by fitting it into the totality of things. Usually the first step is to relax and i maintain you know that these kind of theories promote and give permission to abandon anxiety. that they say it's all right you know, it isn't riding on the egos of civilized people, it isn't up to us to control and understand we are. we are part of a system but the system is in governance of the situation, it is not running out of control, it has not escaped its traces and in a malfunctioning state, it's just that it is a process of winding things up in order to condense them down, in order to push them into another dimensional domain where everything is connected to everything else and therefore everything is at equilibrium and completion.
there it is in a nutshell.
